Question

The market price of a stock is $41.47 and it just paid $4.64 dividend. The dividend is expected to grow at 2.25% forever. What is the required rate of return for the stock?

Answer 1

To find the required rate of return for a stock, you can use the Gordon Growth Model (also known as the Dividend Discount Model for constant growth). This model states that the price of a stock is equal to the next expected dividend divided by the difference between the required rate of return and the growth rate of the dividend.

The formula is as follows:

\[
P_0 = \frac{D_1}{r - g}
\]

Where:
- \( P_0 \) = Current stock price
- \( D_1 \) = Dividend expected next year
- \( r \) = Required rate of return
- \( g \) = Growth rate of dividends

First, we need to calculate \( D_1 \), the dividend expected next year. Since the last dividend paid was $4.64 and it grows at a rate of 2.25%, we calculate \( D_1 \) as follows:

\[
D_1 = D_0 \times (1 + g) = 4.64 \times (1 + 0.0225) = 4.64 \times 1.0225 \approx 4.748
\]

Now we have:
- \( D_1 \approx 4.748 \)
- \( P_0 = 41.47 \)
- \( g = 0.0225 \)

We can now plug these values into the Gordon Growth Model formula to solve for \( r \):

\[
41.47 = \frac{4.748}{r - 0.0225}
\]

Rearranging this equation to solve for \( r \):

\[
41.47(r - 0.0225) = 4.748
\]

\[
41.47r - 0.933075 = 4.748
\]

\[
41.47r = 4.748 + 0.933075
\]

\[
41.47r = 5.681075
\]

\[
r = \frac{5.681075}{41.47} \approx 0.1375 \text{ or } 13.75\%
\]

Thus, the required rate of return for the stock is approximately **13.75%**.